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couldn't it be that it's changing at a slow rate? over a 15 billion year history, this adds up to a significant change in the speed of light.

if c* was the speed of light when t=0 and if it gets multiplied by a factor of 1.0000000001 every millenium, since there have been 15 million millenia (though that would be drawn into question if c is not constant), that would add up to 1.0000000001^(15 10^9)=4.5 times as fast now than it was when t=0.